{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Theory ##\n",
    "\n",
    "Let's say, we have data $X$, which is a matrix of $N$ values, each having\n",
    "dimensionality $p$.\n",
    "Then the covariance matrix $\\Sigma$ of $X$ can be computed as:\n",
    "$$\\Sigma = \\frac{X^T X}{N-1}$$\n",
    "\n",
    "### Eigenvalues of covariance matrix ###\n",
    "We can represent $\\Sigma$ as a decomposition using its **eigenvalue decomposition**:\n",
    "\n",
    "$$\\Sigma = V L V^{-1}$$\n",
    "\n",
    "where $V$ is a matrix of eigenvectors and $L$ is a diagonal matrix of\n",
    "eigenvalues. For every *covariance matrix* $\\Sigma$ the matrix $V$ will\n",
    "actually be a rotation and thus, $V^{-1} = V^T$. Thus:\n",
    "\n",
    "$$\\Sigma = VLV^{T}$$\n",
    "\n",
    "You can see an example of getting the eigenvalues from a covariance matrix in\n",
    "function `plot_cov_ellipse`.\n",
    "\n",
    "### Relation to SVD ###\n",
    "We can express our data $X$ as a decomposition using **SVD**:\n",
    "\n",
    "$$ X = \\mathrm{SVD}(X) = USV^T $$\n",
    "\n",
    "where $U$ is a unitary matrix that holds left-singular vectors, $S$ is a\n",
    "diagonal matrix of singular values and $V$ is a unitary matrix of\n",
    "right-singular vectors.\n",
    "\n",
    "The matrix $V$ is the same as the matrix $V$ from eigenvalue decomposition of\n",
    "$\\Sigma$.\n",
    "\n",
    "This allows us to find the correspondence between singular values of $X$ to the\n",
    "eigenvalues of $\\Sigma$.\n",
    "\n",
    "$$ \\Sigma = \\frac{X^T X}{N-1} = \\frac{(USV^T)^T (USV^T)}{N-1} = \\frac{VSU^{T} USV^T}{N-1} = V \\frac{S^2}{N-1} V^T$$\n",
    "\n",
    "This looks exactly like the eigenvalue decomposition of the covariance matrix $\\Sigma$:\n",
    "\n",
    "$$ V \\frac{S^2}{N-1} V^T = VLV^{T} \\Rightarrow L = \\frac{S^2}{N-1} $$\n",
    "\n",
    "### SVD of covariance matrix ###\n",
    "Singular values *of the covariance matrix $\\Sigma$* are the same as its eigenvalues. The code to check this is in function `compare_eigen_svd`.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Ellipse\n",
    "from IPython.display import display, Math, Latex, Markdown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_cov_ellipse(data, pos, nstd=2, ax=None, **kwargs):\n",
    "    def eigsorted(cov):\n",
    "        W, V = np.linalg.eig(cov)\n",
    "        order = W.argsort()[::-1]\n",
    "        return W[order], V[:,order]\n",
    "    \n",
    "    cov = np.cov(data, rowvar=False)\n",
    "\n",
    "    if ax is None:\n",
    "        ax = plt.gca()\n",
    "\n",
    "    W, V = eigsorted(cov)\n",
    "    display(Markdown('# Eigenvalue decomposition #'))\n",
    "    print(\"eigen vals:\", W)\n",
    "    print(\"eigen vectors:\\n\", V)\n",
    "    theta = np.degrees(np.arctan2(*V[:,0][::-1]))\n",
    "\n",
    "    # Width and height are \"full\" widths, not radius\n",
    "    width, height = 2 * nstd * np.sqrt(W)\n",
    "    ellip = Ellipse(xy=pos, width=width, height=height, angle=theta, **kwargs)\n",
    "\n",
    "    ax.add_artist(ellip)\n",
    "    ax.set_title('From eigenvalues')\n",
    "    return ellip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_svd_ellipse(data, pos, nstd=2, ax=None, **kwargs):\n",
    "    if ax is None:\n",
    "        ax = plt.gca()\n",
    "    centered_data = data - pos\n",
    "    U, S, V_T = np.linalg.svd(centered_data)\n",
    "    V = V_T.T\n",
    "    display(Markdown('# SVD decomposition #'))\n",
    "    print(\"singular vals:\", S)\n",
    "    print(\"singular vectors:\\n\", V)\n",
    "    theta = np.degrees(np.arctan2(*V[:,0][::-1]))\n",
    "\n",
    "    # Width and height are \"full\" widths, not radius\n",
    "    width, height = 2 * nstd * (S / np.sqrt(data.shape[0]))\n",
    "    ellip = Ellipse(xy=pos, width=width, height=height, angle=theta, **kwargs)\n",
    "\n",
    "    ax.add_artist(ellip)\n",
    "    ax.set_title('From singular values')\n",
    "    return ellip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def compare_eigen_svd(data):\n",
    "    display(Markdown('# Eigenvalues vs singular values of a cov matrix #'))\n",
    "    display(Markdown('The eigenvalues should be the same as singular values '\n",
    "                     'when `eig` and `SVD` are applied to a covariance matrix $\\Sigma$'))\n",
    "    cov = np.cov(data, rowvar=False)\n",
    "    W, V_eig = np.linalg.eig(cov)\n",
    "    U, S, V_svd = np.linalg.svd(cov)\n",
    "    display(Markdown('### Eigenvalues of $\\Sigma$'))\n",
    "    print(W)\n",
    "    display(Markdown('### Singular values of $\\Sigma$'))\n",
    "    print(S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "# Eigenvalue decomposition #"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eigen vals: [ 35.66029313  10.04952904]\n",
      "eigen vectors:\n",
      " [[-0.50231364 -0.8646855 ]\n",
      " [-0.8646855   0.50231364]]\n"
     ]
    },
    {
     "data": {
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JwBh8gxGPQEAajrz7rnSZKisbWHpltuSmZysXHgvZ8uxiYcwY2f29847w+dmohzRYZM/T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\noAhfQUFBYZzg/weAj6EXx818ZgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2e0c186b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "# SVD decomposition #"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "singular vals: [ 188.74488825  100.19720309]\n",
      "singular vectors:\n",
      " [[-0.50231364 -0.8646855 ]\n",
      " [-0.8646855   0.50231364]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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muNh/8EyCPcNgdXR8j402AxWugRSB9q7TWLbm3aD+ilDziUbLygHnZ4hkcHWp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1lIHljlcOm5os1hmBiPFofKonHtZT4EDVLLac6I2fkvrklFGDG9wuTsGlF5bN6IRKs9tBHRck8f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\n3xRUXOvzt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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2e0ce2e518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "# Eigenvalues vs singular values of a cov matrix #"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "The eigenvalues should be the same as singular values when `eig` and `SVD` are applied to a covariance matrix $\\Sigma$"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "### Eigenvalues of $\\Sigma$"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 10.04952904  35.66029313]\n"
     ]
    },
    {
     "data": {
      "text/markdown": [
       "### Singular values of $\\Sigma$"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 35.66029313  10.04952904]\n"
     ]
    }
   ],
   "source": [
    "# Generate some random, correlated data\n",
    "points = np.random.multivariate_normal(mean=(20,10), cov=[[18, 12],[12, 30]], size=1000)\n",
    "pos = points.mean(axis=0)\n",
    "plot_size = (6,6)\n",
    "x, y = points.T\n",
    "fig = plt.figure(0, figsize=plot_size)\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(x, y, 'bo')\n",
    "plot_cov_ellipse(points, pos, nstd=3, alpha=0.2, color='blue')\n",
    "plt.show()\n",
    "\n",
    "fig = plt.figure(1, figsize=plot_size)\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(x, y, 'bo')\n",
    "plot_svd_ellipse(points, pos, nstd=3, alpha=0.5, color='orange')\n",
    "plt.show()\n",
    "\n",
    "# compare eigen values and singular values of a cov matrix\n",
    "compare_eigen_svd(points)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
